Question

Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. Flowering plants sell for $8, and nonflowering plants sell for $5. Joey wants to purchase a combination of plants that minimizes cost. Let x represent the number of flowering plants and y represent the number of nonflowering plants.
What are the vertices of the feasible region for this problem?

a. (0,0) (0,36) (24,12)
b. (0,36) (24,12)
c. (0,36) (24,12) (36,0)
d. (24,12) (36,0)

Answer 1

The question is asking to choose among the following choices that states the vertices of the feasible region for the problem and base on my calculation and further research about the said problem, the answer would be letter D. (24,12) and (36,0). I hope you are satisfied with my answer and feel free to ask for more 

Answer 2

Answer:

The vertices of the feasible region for this problem is:

      d.       (24,12) (36,0)

Step-by-step explanation:

Let x denote the number of flowering plants

and y denotes the number of non-flowering plant.

It is given that:

He wants to have at least twice as many flowering plants as nonflowering plants.

This means that the inequality which will be formed is given by:

           $x\geq 2y$

and he must have a minimum of 36 plants in his garden.

This means that the inequality is given by:

                 $x+y\geq 36$

Also,  Flowering plants sell for $8, and nonflowering plants sell for $5.

He wants to t minimizes cost.

so, the optimal function is given by:

Cost  Min. c= 8x+5y

The system is written as:

Optimal function    Min. c= 8x+5y

Constraints             $x\geq 2y----------(1)$

                      and   $x+y\geq 36-------(2)$

Now, we know that the feasible solution is one which satisfy all the constraints.

Hence, we will check each of the options whether they satisfy constraints or not.

a)

   (0,0) (0,36) (24,12)

when we put (0,0) in constraint (2) we get:

           0≥ 36 which is a false relation.

Hence, option: a is incorrect.

b)

     (0,36) (24,12)

when we put (0,36) in the first constraint we get:

         0 ≥ 72

which is again a false identity.

Hence, option: b is incorrect.

c)

(0,36) (24,12) (36,0)

This option is incorrect.

( Because as done in option: b

(0,36) do not satisfy the constraint (1))

d)

             (24,12) (36,0)

• (24,12)

        when we put x=24 and y=12

          we see that it satisfy both the constraint

• (0,36)

     when we  put x=0 and y=36 we will observe that it satisfy both the constraints.

     Hence, the correct answer is: Option: d